What is the length of the shadow?

Question

A 5'6" person walking down the street notices his shadow. If the angle of elevation from the tip of the shadow to the sun is 60 degrees, what is the length of the shadow?

Answer 1

Hello, Bailey 

I am going to start by changing 5ft 6 in. into 5.5 feet, since each foot is equal to 12 inches. 

 

If you draw a right triangle, the height of the person represents the height of the triangle, and the base represents the length of the shadow. The angle of elevation is 60 degrees.  This angle should be opposite the side that measures 5.5 feet.  

 

So, you can see that we are looking for x, which is the shadow of the person.

 

We are going to use the tangent to figure the length of the shadow.

As you might recall, Bailey, tangent=(opposite)/(adjacent). So, we have

 

tan 60= (5.5)/x              The tan of 60= sq. rt. 3, which is 1.7321

1.7321= (5.5)/x.             Multiply both sides by x

1.7321x= 5.5.                 Divide both sides by 1.7321

x= 3.1753  Ft                  Which is about 3 feet 2 in.

                                       3+(.1753ft)(12)=2.1036 in.= 3' 2" approx.

 

Well, there you have it.. Thanks for posting and please rate my answer:).

 

D.Y. Taylor